Orthogonal sets

Orthogonal sets

Lessons

A set of vectors {v1,⋯,vnv_1,\cdots,v_nv​1​​,⋯,v​n​​} in Rn\Bbb{R}^nR​n​​ are orthogonal sets if each pair of vectors from the set are orthogonal. In other words,

vi⋅vj=0v_i \cdot v_j =0v​i​​⋅v​j​​=0

Where i≠ji \neq ji≠j.

If the set of vectors {v1,⋯,vnv_1,\cdots,v_nv​1​​,⋯,v​n​​} in Rn\Bbb{R}^nR​n​​ is an orthogonal set, then the vectors are linearly independent. Thus, the vectors form a basis for a subspace SSS. We call this the orthogonal basis.

To check if a set is an orthogonal basis in Rn\Bbb{R}^nR​n​​, simply verify if it is an orthogonal set.